The Better Baby Buggy Co. has just come out with a new model, the Turbo. The market research department predicts that the demand equation for Turbos is given by q = - 4p + 616, where q is the number of buggies the company can sell in a month if the price is $p per buggy. At what price should it sell the buggies to get the largest revenue? p = $ What is the largest monthly revenue? $

Question

Oompa Loompa

Mathematics

3 January, 16:57

The Better Baby Buggy Co. has just come out with a new model, the Turbo. The market research department predicts that the demand equation for Turbos is given by q = - 4p + 616, where q is the number of buggies the company can sell in a month if the price is $p per buggy. At what price should it sell the buggies to get the largest revenue? p = $ What is the largest monthly revenue? $

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Duarte · Answer 1

In this question, q is the number of buggies the company can sell in a month if the price is $p per buggy. The revenue should be number of buggies sold (q) multiplied by the price (p). The equation would be:

revenue = p * q

revenue = p * (-4p + 616) = - 4p^2 + 616p

The maximum revenue should be in the peak of the graph. The calculation would be:

-4p^2 + 616p

-4*2 p^2-1 + 616*1 p^1-1=0

-8p + 616=0

8p = 616

p=77

Put p=77 in the revenue equation would result

revenue = - 4p^2 + 616p

revenue = - 4 (77^2) + 616 (77) = - 23716 + 47432 = $23716